The date shown by $date is wrong, what is the difference between $date and $modif?

The $date variable is either the document creation date or the date of the remote server depending on what the later returns.

The $modif variable is the date when the document was modified for the last time. Some servers do not return the correct date and do not respond to if-Modified-Since used to query modified documents only. This is common to dynamically generated documents such as CGIs.

When the server returns no or a bogus date, Alkaline will use the first date available or the today's date for either or both of the $modif and the $date variables.

To find out what your server returns, use telnet to connect to it and request a page. Note the Last-Modified and the Date headers in the example below.
$ telnet www.vestris.com 80 
Trying 66.33.25.221... 
Connected to vestris.com. 
Escape character is '^]'. 
GET / HTTP/1.1 
host: www.vestris.com 

HTTP/1.1 200 OK 
Date: Fri, 05 Oct 2001 04:50:25 GMT 
Server: Apache/1.3.9 (Unix) (Red Hat/Linux) 
Last-Modified: Mon, 27 Aug 2001 02:23:28 GMT 
ETag: "9d371-751-3b89af20" 
Accept-Ranges: bytes 
Content-Length: 1873 
Content-Type: text/html 
    
...